2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71166we show that the space of metrics of positive scalar curvature on a manifold is, when nonempty, homotopy equivalent to a space of metrics of positive scalar curvature that restrict to a fixed metric near a given submanifold of codimension greater or equal than 3. Our main tool is a parameterized version of the Gromov-Lawson construction, which was used to show that the existence of a metric of positive scalar curvature on a manifold was invariant under surgeries in codimension greater or equal than 3.22 pages, 5 EPS figures; fixed problems with bibliographyGeometric TopologyDifferential Geometry58D17; 57R65text